She let the information slip while chatting to a volunteer at the centre in southeast London, run by a charity working with young families.
“I told her she is beautiful and that she’s got a tiny little bump. I asked when her baby is due and she said mid-to-end of April,” volunteer Christine Osborne told reporters after speaking to her.
Contacted by AFP, Kensington Palace, the British royal couple’s official residence in central London, declined to comment on the report.
Kate is already mother to 18-month-old Prince George, the third in line to the throne. Royal officials announced she was pregnant with her second child in September.
The £35 (48 euro, $52) black polka dot maternity dress she wore during her visit on Wednesday, from online retailer Asos, sold out within 30 minutes of her public appearance. (AFP)